Related papers: The full basis theorem does not imply analytic wel…

A description of physical reality in which wholeness is the foundation is discussed along with the motivation for such an attempt. As a possible mathematical framework within which a physical theory based on wholeness may be expressed,…

We apply, in the context of semigroups, the main theorem from~\cite{higjac} that an elementary class $\mathcal{C}$ of algebras which is closed under the taking of direct products and homomorphic images is defined by systems of equations. We…

There is a model of ZF with a $\Delta^1_3$ definable Hamel basis in which $AC_\omega(R)$ fails.

Let $G$ be a finitely generated torsion-free nilpotent group. The representation zeta function $\zeta_G(s)$ of $G$ enumerates twist isoclasses of finite-dimensional irreducible complex representations of $G$. We prove that $\zeta_G(s)$ has…

Assume $\mathcal{C}$ is the class of all linear orders $L$ such that $L$ is not a countable union of well ordered sets, and every uncountable subset of $L$ contains a copy of $\omega_1$. We show it is consistent that $\mathcal{C}$ has…

We introduce and study some variants of a notion of canonical set theoretical truth. By this, we mean truth in a transitive proper class model $M$ of ZFC that is uniquely characterized by some $\in$-formula. We show that there are…

Sets with atoms serve as an alternative to ZFC foundations for mathematics, where some infinite, though highly symmetric sets, behave in a finitistic way. Therefore, one can try to carry over analysis of the classical algorithms from finite…

In this article, which is dedicated to my friend and colleague Boris Zilber on the occasion of his 75th birthday, I put forward a strategy for proving his quasiminimality conjecture for the complex exponential field. That is, for showing…

In this article we proved so-called strong reflection principles corresponding to formal theories Th which has omega-models. An posible generalization of the Lob's theorem is considered.Main results is: (1) let $k$ be an inaccessible…

The proper Class $\bf{No}$ of all Conway's numbers $\cite{l3}$ is considered as a region of investigation. It turns out to be a total ordered Field (i.e., a field whose domain is a proper Class) and this totally, or linear ordered Class,…

We show it is consistent with $\ZFC$ that there is an everywhere Kurepa line which is order isomorphic to all of its dense $\aleph_2$-dense suborders. Moreover, this Kurepa line does not contain any Aronszajn suborder. We also show it is…

We present for static density functional theory and time-dependent density functional theory calculations an all-electron method which employs high-order hierarchical finite element bases. Our mesh generation scheme, in which structured…

Assuming $M_1$, the canonical inner model with one Woodin cardinal exists, we construct a model in which the nonstationary ideal on $\omega_1$ is $\aleph_2$-saturated, $\Delta_1$-definable with $\omega_1$ as the only parameter and there is…

Let $X$ be a perfect, compact subset of the complex plane. We consider algebras of those functions on $X$ which satisfy a generalised notion of differentiability, which we call $\mathcal{F}$-differentiability. In particular, we investigate…

The fundamental tension between availability and consistency shapes the design of distributed storage systems. Classical results capture extreme points of this trade-off: the CAP theorem shows that strong models like linearizability…

In 1958, Helson and Lowdenslager extended the theory of analytic functions to a general class of groups with ordered duals. In this context, analytic functions on such a group $G$ are defined as the integrable functions whose Fourier…

We investigate an analogue of the Wedderburn principal theorem for associative conformal algebras with finite faithful representations. It is shown that the radical splitting property for an algebra of this kind holds if the maximal…

Let G be a quasisimple algebraic group over an algebraically closed field of characteristic p>0. We suppose that p is very good for G; since p is good, there is a bijection between the nilpotent orbits in the Lie algebra and the unipotent…

We prove the following two results. Theorem A: Let alpha be a limit ordinal. Suppose that 2^{|alpha|}<aleph_alpha and 2^{|alpha|^+}<aleph_{|alpha|^+}, whereas aleph_alpha^{|alpha|}>aleph_{|alpha|^+}. Then for all n< omega and for all…

In this paper, a generalized version of the von Neumann universe known as the total universe is proposed to formally introduce non-well-founded sets that include infinitons, semi-infinitons and quasi-infinitons in Russell's paradox. All…